Linear, Polynomial and Exponential Growth Compared Worksheet with Answer Key

What's on the worksheet

1. For each pair, say which function is bigger for large x and name the result that tells you.
   0.001(1.1)^x or 1000x^5x^4 or 50x^3 + 10005(0.9)^x or 0.01x\dfrac{2^x}{x^{10}} or x^32^x or \dfrac{3^x}{x^2}
2. Compare average rates of change of a quadratic and an exponential over several intervals.
3. Show the step factor of a power times a shrinking exponential and explore its pattern.
4. Show an inequality fails at 3 but holds at 4, then prove it for every whole number from 4.
5. Word problem: three designs for the experience points needed to reach each game level.